The Batman Season 2 marked the end of what they could do with the latest Bat-concept. They needed to expand or go in a different direction. In the third season, they did both.... but with mixed results.
The fact that Bat-girl made it to the BAtcave before Robin is debatable. Since everything in this serie is a re-design of the original concept, it is acceptable. The too-young Batgirl is no Yvonne Craig. They gave her an annoying voice and is way too small to be believable. Kind of like the Robin in Teen Titans. Batman and Batgirl look like they are in parallel universe and you do not get into their personality feud. The Batgirl concept is forced into us, the same way she wants to invade Batman's bubble. She has the same dressing up routine as the BAT, but it left me cold. Not sure if I am eatching a early Saturday morning cartoon or something more cerebral...
It is too bad, because the writing is getting better at a steady pace. Storylines are more intricate and multi-layered. The car racing episode is fabulous and so is the one with the Joker's sidekick is touching . Batgirl's humor feels warm and witty, almost welcomed.
I cannot recommend the S3 to anyone, except if do not want to miss antrhing rhat would impair the fun of watching the fantastic fourth season. T is sort of an introduction to S4.